Aircraft: PC-12
Phase of flight: Parked
Anomaly: Aircraft Equipment Problem Critical; Deviation / Discrepancy - Procedural Maintenance; Deviation / Discrepancy - Procedural Published Material / Policy; Flight Deck / Cabin / Aircraft Event Smoke / Fire / Fumes / Odor

In the morning we were assigned Aircraft X; fresh out of phase inspection. I had divided the flights for the day; and flights I was to be PF (Pilot Flying). Aircraft X was in the maintenance hangar at ZZZ. They (Maintenance) pulled it out and left it in front of the terminal. I completed my exterior check per the checklist and interior/exterior security sweep with nothing abnormal. SIC did interior preflight. I pinned the W&B (Weight and Balance) shortly afterwards and passengers were loaded when we received pin from Dispatch. Started Aircraft X following appropriate checklists and flows with no abnormalities; until the pusher test. The pusher system would not activate and pull the yoke after three tests. I notified [Name] that we will shut down and deplane passengers. I called Maintenance Control as that is the protocol prior to talking to the Local Maintenance. After the call with Maintenance Control; the local mechanic came out to troubleshoot and found that ZZZ Maintenance had not reset the pusher circuit breaker. Pusher tested correctly then for him. They contacted Maintenance Control and after informed me we are cleared to go. Passengers were boarded and we departed ZZZ to ZZZ1. All procedures and checklists were followed per company docs. All indications were normal and performance was as expected. In ZZZ1 the aircraft was fueled and nothing abnormal was noted on post flight. We departed ZZZ1 for ZZZ2. During the flight to ZZZ2; all procedures and checklists were followed per [Company Docs] and was also uneventful. Once in ZZZ2 and after passengers were deplaned; I exited Aircraft X and was about to begin my post flight inspection; I immediately noticed something unusual. There was damage to the left front upper engine cowling just behind the exhaust. There was a large hole with burn marks around it and black soot extending rearward. After checking the temperature of the rear cowling; I opened the cowling which revealed more soot. At first glance; we were both unable to find the source. After some peeking toward the front engine area from rear cowling area; First Officer noticed there was threaded open hole that lined up with the hole damage on front cowling. He showed me this finding and I included that in my initial call to Maintenance Control. While still on the phone with Maintenance Control; ZZZ2 Maintenance had showed up. They loudly proclaimed their disbelief. Since I was waiting for Maintenance Control to type all this in; I went outside to see what the commotion was about. At least four maintenance personnel were looking at Aircraft X cowling and looked shocked. They said that we are lucky to be alive. The igniter was hanging and according to Maintenance there was a potential for combustion inside the cowling. They said they could not believe this happened especially after a phase. I finished with Maintenance Control and Aircraft X was grounded. We were swapped into [another aircraft] and continued the route. First Officer notified our Chief Pilot about the ordeal. As of this time nothing came out of this at the company level. It seems to be swept under the rug. I learned that even if it's hard to inspect the front engine area; I need to take even more time preflighting to possibly catch these things. Especially after service by Maintenance. PC-12 Captain reported discovering burn marks on the cowl during post flight inspection due to improper maintenance work on the engine.